Question 814889
Let d = diameter of the base.
h=d+2 where h is height.

Volume, {{{v=h(1/3)pi*r^3}}} and here, {{{r=(1/2)d}}} so you could use volume formula as {{{v=(d+2)(1/3)pi*(1/2)^3*d^3}}}
{{{v=(d+2)(1/24)pi*d^3}}}
.
and you would want to solve for d, because you were already given v=8 cubic inches.


{{{v=d(pi/24)d^3+2(pi/24)d^3}}}
{{{v=(pi/24)d^4+2(pi/24)d^3}}}
{{{highlight((pi/24)d^4+(pi/12)d^3-8=0)}}}, using the given v=8.


At this extent, one would prefer to use a graphing calculator or some other software program to handle that cubic equation.  The value of d which satisfies the equation would be (for positive d) the diameter...


Trying the function in Google as {{{y=(pi/24)x^4+(pi/12)x^3-8}}}, zooming in, the root of y appears to be 2.403, or something very very near it.